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An automorphism is an isomorphism from an object to itself, and which also preserves the objects structure .

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Automorphisms of vector spaces and the complex numbers without choice

.\ AL19(F))⇒AC$, in particular, the strengthening of $B(ℂ)$ to $AL19(ℂ)$ does imply AC and hence imply that there are wild automorphisms for $ℂ$. … .\ AL20(F))⇒MC$ (which over ZF implies $AC$), and hence the dual strengthenin of $B(ℂ)$ to $AL20(ℂ)$ also imply that there are wild automorphisms for $ℂ$ (although from quick glance over [3,4] I couldn't …
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